symbols wrote:Mr. Black, Mr. Gray, and Mr. White are fighting in a truel. They each get a gun and take turns shooting at each other until only one person is left. Mr. Black, who hits his shot 1/3 of the time, gets to shoot first. Mr. Gray, who hits his shot 2/3 of the time, gets to shoot next, assuming he is still alive. Mr. White, who hits his shot all the itime, shoots next, assuming he is also alive. The cycle repeats. If you are Mr. Black, where should you shoot first for the highest chance of survival?
Best strategy is to eliminate White first, who has a 100% success rate. Black might then get a second chance at shoot-out with Gray.
Black has a accuracy of 1/3. That works out to 2/3 chance of hitting a target he doesn't intend.
Black should therefore shoot at Gray knowing he has a 2/3 chance of hitting White.
Life is short. Live passionately.